A structural model for credit risk with switching processes and synchronous jumps

This paper studies a switching regime version of Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a switching Lévy process. The novelty of this approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, two models are presented. In the first one, the default happens at bond maturity, when the firm's value falls below a predetermined barrier. In the second version, the firm can enter bankruptcy at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. With synchronous jumps, the firm's asset and state processes are no longer uncorrelated. Finally, some econometric evidence that switching Lévy processes, with synchronous jumps, fit well historical time series is provided.     

A model for interest rates with clustering effects

We propose a model for short-term rates driven by a self-exciting jump process to reproduce the clustering of shocks on the Euro overnight index average (EONIA). The key element of the model is the feedback effect between the absolute value of jumps and the intensity of their arrival process. In this setting, we obtain a closed-form solution for the characteristic function for interest rates and their integral. We introduce a class of equivalent measures under which the features of the process are preserved. We infer the prices of bonds and their dynamics under a risk-neutral measure. The question of derivatives pricing is developed under a forward measure, and a numerical algorithm is proposed to evaluate caplets and floorlets. The model is fitted to EONIA rates from 2004 to 2014 using a peaks-over-threshold procedure. From observation of swap curves over the same period, we filter the evolution of risk premiums for Brownian and jump components. Finally, we analyse the sensitivity of implied caplet volatility to parameters defining the level of self-excitation.     

Strategic asset?allocation with switching dependence

This paper revisits the problem of the strategic asset allocation between stocks and bonds. The novelty of our approach is to model the influence of economic cycles on the marginal distributions of asset returns and their dependence structure by a single hidden Markov chain. After a brief review of selected statistical distributions (Student’t and Weibull) and copulas (elliptic and Archimedian), we describe how the switching regime model is calibrated using two indices: the CAC 40 for stocks and the SGI Bond 10 years, for bonds. We then propose a dynamic investment policy based on the estimated probabilities of sojourn in each state of the Markov chain. Even though the Markov chain ruling the assets dynamics is hidden, a Bayesian procedure can be used to infer the probabilities of being in a certain state of the economy. The asset allocation can then be adapted to provide the highest yield given the most likely state. Having calibrated and estimated the parameters of the model, the performance of static and dynamic strategies are compared by conducting Monte Carlo simulations. Our results show that dynamic strategies, which exploit the additional information relating the probable regime state, perform better than static policies with a limited risk and an acceptable number of reallocations.     

An intensity model for credit risk with switching Lévy processes

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Lévy process. This model presents several interesting features. First, as Lévy processes encompass numerous jump processes, our model can duplicate the sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as the parameters of the Lévy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors.     

A self-exciting switching jump diffusion: properties,calibration and hitting time

A way to model the clustering of jumps in asset prices consists in combining a diffusion process with a jump Hawkes process in the dynamics of the asset prices. This article proposes a new alternative model based on regime switching processes, referred to as a self-exciting switching jump diffusion (SESJD) model. In this model, jumps in the asset prices are synchronized with changes of states of a hidden Markov chain. The matrix of transition probabilities of this chain is designed in order to approximate the dynamics of a Hawkes process. This model presents several advantages compared to other jump clustering models. Firstly, the SESJD model is easy to fit to time series since estimation can be performed with an enhanced Hamilton filter. Secondly, the model explains various forms of option volatility smiles. Thirdly, several properties about the hitting times of the SESJD model can be inferred by using a fluid embedding technique, which leads to closed form expressions for some financial derivatives, like perpetual binary options.